Technically speaking, at the level of being, a site x proves itself paradoxical in its
being a reflexive multiple, meaning it is an element of itself, it ‘auto-belongs’ (that
is, x ∈ x).10 In its counting of itself in itself the site thus constitutes a supernumerary
term—it is, as Badiou puts it, an ‘ultra-one’—and is as such, by dint of
the axiom of foundation (which effectively prohibits a set’s belonging to itself),
ontologically illegal. In transgressing the laws of being, the site must accordingly
vanish. Lastly—and this really is key—in its giving its very being a value of existence,
a site temporarily bridges the fissure separating ‘being’ from ‘being-there’,
which is to say it involves “the instantaneous revelation of the void that haunts
multiplicities”:11 the site convokes or ‘brings forth’ what is void in the situation, it
presents what had been altogether unrepresented (by the state); in short, it brings
into existence what had previously failed to appear.